5038
J. Phys. Chem. B 1998, 102, 5038-5041
Coupling of Normal and Transverse Motions during Frictional Sliding Manfred Heuberger Laboratory for Surface Science and Technology, ETH, CH-8092 Zu¨ rich, Switzerland
Carlos Drummond and Jacob Israelachvili* Department of Chemical Engineering, and Materials Department, UniVersity of California, Santa Barbara, California 93106 ReceiVed: May 19, 1998
Using a surface forces apparatus, modified for measuring friction forces while simultaneously inducing normal (out-of-plane) vibrations between two boundary-lubricated sliding surfaces, we observe load- and frequencydependent transitions between a number of “dynamic friction” states. In particular, we found regimes of vanishingly small friction at interfacial oscillation amplitudes below 1 Å. The phenomenon is shown to have a molecular origin but requires the molecular relaxation time to be faster than the mechanical resonance time of the macroscopic system. A parallel computer simulation study (Gao et al. J. Phys. Chem. B 1998, 102, 5033) provides a theoretical basis for the observed phenomenon and indicates its broader generality. Our results also point to novel methods for realizing ultralow friction in mechanical devices.
Introduction The dynamics of molecular relaxation processes at an interface are a crucial factor in determining the static and kinetic friction forces of boundary-lubricated systems and of polymers or complex fluids trapped between two shearing surfaces.2-10 Such systems manifest a complex spectrum of dynamic energy dissipation as a function of sliding velocity, load, and temperature, in which the kinetic friction often exhibits a maximum when the system is driven (sheared) at the same speed or frequency at which a specific molecular relaxation appears.11-13 While the above phenomenon is now well-understood,6 the related phenomenon of the coupling between orthogonal energy modes is not. Artificially induced vibrations, both parallel and normal to the sliding direction, have long been used empirically to reduce frictional energy dissipation in machinery,14,15 and a number of simple models14,16 are available for describing the transverse response to various types of dynamic modulations of the load. In these models, the idea is that over some fraction of the oscillation the surfaces separate from contact and that during this period the friction is zero. Consequently, the timeaveraged friction force is reduced below its value in the absence of vertical oscillations. This mechanism requires large driving amplitudes (sufficient to separate the surfaces even when they are in contact under a compressive load) and is essentially a macroscopic effect, unrelated to the adhesion and friction processes occurring at the microscopic and molecular levels. The experiments described here show that ultralow kinetic friction can also be produced by introducing fast subnanometer perturbations normal to the plane of sliding during which time sliding proceeds with the two surfaces remaining in contact. Experimental Methods The friction experiments were performed between two identical surfaces coated with a 3.5 nm thick bilayer of the “boundary lubricant” surfactant tridecafluoro-1,1,2,2-tetrahydrooctyl-1-trichlorosilane, self-assembled onto freshly cleaved
atomically smooth mica substrate surfaces from vapor.18 This boundary lubricant layer was chosen because it produces highly uniform, molecularly smooth surface layers that exhibit medium to low friction and a molecular relaxation (stick-slip transition) at low frequencies.19 The composition and structure of the deposited layers were verified using scanning auger electron spectroscopy, atomic force microscopy, and multiple beam interferometry (MBI). The tribological measurements were carried out using a surface forces apparatus (SFA MK II) with additional attachments for (i) driving the surfaces laterally past each other (bimorph slider20), (ii) measuring the lateral force response (friction device21), and (iii) vibrating one surface normally at varying amplitudes and frequencies using a piezoelectric crystal transducer. The surface geometry, including the contact area, the boundary layer thickness, and the refractive index of the boundary film, were monitored using MBI,22 and the moving “FECO” fringes were recorded on S-VHS tape for later analysis. This procedure allowed direct observation and measurement of the dynamic thickness and dilatency of the boundary layers at the angstrom resolution level with a time resolution of 30 ms throughout an experiment. A schematic figure of the experimental setup is shown in Figure 1, where we may note that the transducer or driving amplitude z0, the resulting dilatency ∆D, and the perturbation amplitude z are three separate quantities. The mechanical resonance of the apparatus (any apparatus) plays an important role in determining the way mechanical energy from the transducer (engine) is coupled to the boundary layers (sliding surfaces). An analysis of the general equations of motion is given by Burnham et al.,23 which, for the SFA, leads to the typical coupling-ratio characteristics depicted in Figure 2A. We note that the coupling ratio diverges around 930 Hz, which represents the main resonance frequency ν0 of the apparatus. Above about 2 kHz the coupling ratio converges asymptotically toward 1. In a more realistic model, one would expect additional features in the coupling spectrum due to adhesion, surface damping, and other energy-dissipating mech-
S1089-5647(98)02314-1 CCC: $15.00 © 1998 American Chemical Society Published on Web 06/06/1998
Letters
Figure 1. Schematic representation of the SFA experiment for the simultaneous measurement of normal load, L, and lateral friction force, F, between two surfaces sandwiching boundary layers of “unperturbed” thickness, D0. The upper surface is mounted on a transducer that oscillates at an amplitude z0 and frequency ν, which produces the “perturbation” z at the boundary layers causing them also to dilate by ∆D to a mean thickness of D ) (D0 + ∆D). The layer thickness D and dilatency ∆D were monitored during experiments using MBI. The difference (z - z0) translates into a modulation of the load of ∆L ) (z - z0)KL at the surfaces. Typical experimental values were the following: stiffness of friction force-measuring springs, KF ) 480 N/m; stiffness of load-measuring springs, KL ) 550 N/m; substrate stiffness, KS ≈ 4.21 × 106 Pa; unperturbed thickness of boundary layers, D0 ) 7 nm; transducer (driving) amplitude, z0 ) 5 nm; perturbation amplitude, z < 1 Å; frequency range, ν ) 0-10 kHz; static load, L ) 0-20 mN, load modulation at surfaces, ∆L < 0.1 mN, sliding speed, V ) 0-1 µm/s; molecular contact area, A ≈ 1000 µm2.
anisms occurring at different resonant frequencies. We also draw attention to the fact that the frequency of the main resonance ν0 is essentially determined by the compliance of the substrates’ surfaces KS. The load- and friction-measuring springs, KL and KF, have much lower and resonant frequencies, ∼60 and ∼200 Hz, as measured when the surfaces are completely disengaged. Results Before applying any normal oscillation, i.e., during “unperturbed” sliding, the measured kinetic friction coefficient, defined here as the slope of the F(L) curve, is µ0 ) dF/dL ) 0.48 (Figure 3). The kinetic friction force, F, increases with sliding velocity, V, typically by 50% over a 10-fold increase in V (e.g., from 60 to 600 nm/s). This velocity dependence is indicative of a dynamic energy dissipation mechanism in the boundary layers. Also, there is a finite kinetic friction at zero load, L ) 0, which indicates the presence of attractive forces (adhesion) between the layers, as expected and previously seen with smooth boundary layers.24 Figure 3 also illustrates the dramatic effects on the friction force, F, when the interface is oscillated normal to the sliding direction at different loads, L, and constant driving frequency, ν. Force vs load curves are shown at two different frequencies: at ν ) ν0 ) 929 Hz, coinciding with the main apparatus resonance, and at ν ) 5 kHz, which falls in the high-frequency regime (ν . ν0) where the coupling ratio is 1 (Figure 2A). It is important to point out that owing to the small driving amplitudes, the strong self-adhesion of the surfaces, and the large externally applied compressive loads, the two surfaces appear to remain in contact during sliding at all the frequencies and loads studied, except at the main resonance where the film dilated significantly and the flattened surfaces became rounded. This could be discerned from the FECO fringe positions as described below (Figure 4). From the data presented in Figure 3, it is possible to identify at least three different response regimes exhibiting low,
J. Phys. Chem. B, Vol. 102, No. 26, 1998 5039
Figure 2. (A) Simple mechanical model20 for predicting the mechanical coupling between the transducer and the boundary layer, where adhesion and damping effects are neglected. The model assumes a variable input element (the transducer) in series with the surface compliance KS followed by the mass m of the lower surface and compliance of the load measuring spring KL (cf. Figure 1). After analysis of the equations of motion and inserting the appropriate values for the SFA, the model predicts a “main” resonance at ν0 ) 930 Hz which is determined mainly by the stiffest spring (the surface compliance). (B) Measured kinetic friction force versus driving frequency, exhibiting a rich spectrum, especially at frequencies exceeding the main resonance, where the theoretical coupling ratio is 1.0. Ultralow friction was observed at the main resonance, and secondary maxima and minima were observed at higher frequencies. The frequency range was scanned at random in order to avoid systematic effects.
Figure 3. Kinetic friction force F measured as a function of the applied load L in three different dynamic situations (ν ) 0, 930, and 5000 Hz). The lateral sliding driving velocity was V ) 58 nm/s in all three cases, which is above the critical stick-slip velocity Vc. If the piezomodulation is present, the system exhibits at least three different friction coefficients. In regime I, we observe near-zero kinetic friction and the friction coefficient µI < 0.01 is below our detection limit. Regimes II and III exhibit friction coefficients of µII ) 0.16 and µIII ) 0.62. MBI reveals that the perturbation amplitude z0 and dilatency ∆D are maximum at ν ≈ ν0 ≈ 930 Hz, but their magnitude also depend on the load. The crossover from regime I into regime II coincides with the point where the perturbation amplitude and dilatency become undetectable ( ν0). The inserts are schematic drawings of the changing surface and layer geometries at rest and during oscillatory sliding as visualized by MBI.
after switching off the oscillationssa similar relaxation time to that found for the friction forces. Thus, both the friction force and the dilatency were found to be reproducible, reversible, and correlatedsrelaxing back to their original (unperturbed) values at similar rates after the oscillations were turned off. To ascertain how much of the observed effects are due to the mechanical properties of the apparatus and how much are due to the boundary layers, similar experiments were conducted with two different boundary lubricant fluids. In these, two untreated mica surfaces were contacted either in bulk water or with hexane liquid capillary condensed around the contact area. In both of these cases, the surfaces were sheared with a thin film of liquid, of thickness ∼5-10 Å, between them. Preliminary results on these systems show a large reduction in the friction at the main resonance frequency, ν0, similar to what was measured with the surfactant layer, and further lowerings in the friction forces at higher frequencies that had quite different spectra from that of the surfactant layer. These results confirm that the effects observed depend both on the mechanical properties of the “system” and on the molecular properties of the boundary layers at the interface.
interest because of its ultralow kinetic friction force and very low friction coefficient (µI < 0.01). This regime persists up to a load of L ) 7 mN where the friction force F is still 1, i.e., when ν > 1/τr. However, as pointed out by Gao et al.,1 the distinction between solidlike and liquidlike films, although useful for conceptualizing these transitions,24-26 should not be taken too far, since the molecular ordering and structure of the different dynamic states adopted by confined films during shear are likely to be quite different from their bulk, three-dimensional counterparts. For surfactant boundary monolayers, the main relaxation time τr, which is also the lowest or principal relaxation, can be quite long (typically τr >1 ms) and can be estimated from the critical velocity Vc at which stick-slip sliding goes over to smooth sliding.24 For the boundary monolayers studied here, the critical velocity (which also depends on the temperature and the load) was found to lie in the range Vc ) 50-500 nm/s. Assuming that the characteristic length is of molecular dimensions, δ ≈ 1 nm, we obtain for the characteristic relaxation time of the boundary layers τ ) τr ) δ/Vc ≈ 2-20 ms (corresponding to νr ) 50-500 Hz). On the basis of the results of the computer simulations,1 the driving conditions at which mechanical coupling is expected to become effective is at perturbation amplitudes (at the interface) greater than ∼1 Å and driving frequencies ν greater than 50-500 Hz. The results of the computer simulations1 appear to be consistent with the experimental results reported here and suggest the following scenario: (1) At low driving frequencies (ν < ν0), the kinetic friction force is the same as in the absence of oscillations; this is because the perturbation amplitude at the interface is small (cf. Figure 2A) even though at driving frequencies ν above νr ≈ 500 Hz there is already the potential for efficient coupling with the interface. (2) At ν ) ν0 ) 930 Hz, the effect on the friction is maximal because the perturbation amplitude is at a maximum (cf. Figure 2A) and the driving frequency is now greater than νr. (3) At ν > ν0, since also ν > νr, there is good dynamic coupling but only weak amplitude coupling, although still better than at ν < ν0 (cf. Figure 2A). The resulting effect in this highfrequency regime is a complex spectrum with various maxima and minima whose positions appear to depend on the higher frequency relaxation processes of the boundary layers rather than of the apparatus (note that the principal relaxation at νr ≈ 50-500 Hz is the lowest frequency one). Concluding Remarks We have demonstrated the feasibility of attaining ultralow friction by introducing a fast oscillatory perturbation normal to the sliding plane. Low friction can be achieved by perturbation amplitudes (at the surfaces) of order
